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Mathematics > Analysis of PDEs

arXiv:2205.12336 (math)
[Submitted on 20 May 2022 (v1), last revised 7 May 2023 (this version, v2)]

Title:Construction of GCM hypersurfaces in perturbations of Kerr

Authors:Dawei Shen
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Abstract:This is a follow-up of \cite{KS:Kerr1} on the general covariant modulated (GCM) procedure in perturbations of Kerr. In this paper, we construct GCM hypersurfaces, which play a central role in extending GCM admissible spacetimes in \cite{KS:main} where decay estimates are derived in the context of nonlinear stability of Kerr family for $|a|\ll m$. As in \cite{KS}, the central idea of the construction of GCM hypersurfaces is to concatenate a $1$--parameter family of GCM spheres of \cite{KS:Kerr1} by solving an ODE system. The goal of this paper is to get rid of the symmetry restrictions in the GCM procedure introduced in \cite{KS} and thus remove an essential obstruction in extending the results to a full stability proof of the Kerr family.
Comments: 113 pages, 2 figures, minor improvements, accepted in Annals of PDE. arXiv admin note: substantial text overlap with arXiv:1911.00697 by other authors
Subjects: Analysis of PDEs (math.AP); General Relativity and Quantum Cosmology (gr-qc); Differential Geometry (math.DG)
Cite as: arXiv:2205.12336 [math.AP]
  (or arXiv:2205.12336v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2205.12336

Submission history

From: Dawei Shen [view email]
[v1] Fri, 20 May 2022 21:53:19 UTC (102 KB)
[v2] Sun, 7 May 2023 07:24:56 UTC (287 KB)
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